It's not always easy to see the broken filament, or at least didn't used to be (I've not really examined many in detail recently).
As a kid in the 80s, I used to work in my dad's hardware shop and people regularly used to bring in lights that didn't work. We had a little test area set up where we would put each bulb in turn to find out which one(s) wouldn't light.
I used to use an ohm meter and a binary search algorithm to find the broken bulb in the series strands (waaaaay back in the day). My dad gave me the task as a challenge. I was quite young and into electronics, but it was before I had access to computers (or even calculators for that matter).
As a kid in the 80s, I used to work in my dad's hardware shop and people regularly used to bring in lights that didn't work. We had a little test area set up where we would put each bulb in turn to find out which one(s) wouldn't light.